Numerical solutions of integro-differential equations and application of a population model with an improved Legendre method

YÜZBAŞI Ş., Sezer M., Kemanci B.

APPLIED MATHEMATICAL MODELLING, vol.37, no.4, pp.2086-2101, 2013 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 4
  • Publication Date: 2013
  • Doi Number: 10.1016/j.apm.2012.05.012
  • Journal Name: APPLIED MATHEMATICAL MODELLING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2086-2101
  • Keywords: Population model, Integro-differential equations, Improved Legendre collocation method, Legendre polynomials, Numerical solutions, VOLTERRA INTEGRAL-EQUATIONS, TAYLOR COLLOCATION METHOD, POLYNOMIAL SOLUTIONS, GALERKIN METHODS, HYBRID LEGENDRE, BLOCK-PULSE, 2ND KIND, SYSTEM, CHEBYSHEV, FORM
  • Akdeniz University Affiliated: Yes

Abstract

In this paper, an improved Legendre collocation method is presented for a class of integro-differential equations which involves a population model. This improvement is made by using the residual function of the operator equation. The error differential equation, gained by residual function, has been solved by the Legendre collocation method (LCM). By summing the approximate solution of the error differential equation with the approximate solution of the problem, a better approximate solution is obtained. We give the illustrative examples to demonstrate the efficiency of the method. Also we compare our results with the results of the known some methods. In addition, an application of the population model is made.

In this paper, an improved Legendre collocation method is presented for a class of integro-differential equations which involves a population model. This improvement is made by using the residual function of the operator equation. The error differential equation, gained by residual function, has been solved by the Legendre collocation method (LCM). By summing the approximate solution of the error differential equation with the approximate solution of the problem, a better approximate solution is obtained. We give the illustrative examples to demonstrate the efficiency of the method. Also we compare our results with the results of the known some methods. In addition, an application of the population model is made. (C) 2012 Elsevier Inc. All rights reserved.